Question 1

How do I calculate the area of a triangle?

Accepted Answer

The most common formula is: Area = ½ × base × height. If you know three sides, use Heron's formula: Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 is the semi-perimeter. This calculator uses the appropriate formula based on your inputs.

Question 2

What are the types of triangles?

Accepted Answer

By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal). By angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°). A triangle can be both — e.g., an isosceles right triangle has two equal sides and one 90° angle.

Question 3

What is Heron's formula?

Accepted Answer

Heron's formula calculates a triangle's area using only its three side lengths. First find the semi-perimeter s = (a + b + c) / 2, then Area = √(s × (s-a) × (s-b) × (s-c)). It's named after Hero of Alexandria and works for any triangle shape.

Question 4

How do you find a missing angle in a triangle?

Accepted Answer

If you know two angles, the third is 180° minus their sum. If you know sides, use the Law of Cosines: cos(A) = (b² + c² - a²) / (2bc). If you know one side and its opposite angle plus another side, use the Law of Sines: sin(A)/a = sin(B)/b.

Question 5

What is the Law of Sines?

Accepted Answer

The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are side lengths and A, B, C are their opposite angles. It's useful when you know an angle-side pair plus one other value (ASA, AAS, or SSA cases). Note that SSA can give two possible solutions.

Question 6

What is the Pythagorean theorem?

Accepted Answer

The Pythagorean theorem states that in a right triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle). It's used to find missing sides in right triangles. For example, if a=3 and b=4, then c=5. This only applies to right triangles.

Question 7

How do I calculate the height of a triangle?

Accepted Answer

The height (altitude) from side c is: h = 2 × Area / c. Since Area = ½ × c × h, rearranging gives h = 2A/c. This calculator computes all three heights automatically. For a right triangle, the two legs serve as heights for each other.

Question 8

What is a median of a triangle?

Accepted Answer

A median is a line from a vertex to the midpoint of the opposite side. Every triangle has three medians, which intersect at the centroid (the center of mass). The median length from vertex A to side a is: mₐ = ½√(2b² + 2c² - a²). This calculator computes all three medians.

Triangle Calculator

Input Method

Triangle Diagram

Results

Triangle Calculator

Input Method

Triangle Diagram

Results

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